How can I use GroupMe to broadcast messages with no replies?

There is no way to send broadcast/blast/one-way messages using GroupMe. GroupMe is reply-all by default, and there's no way to change that.

Whenever anyone in the group replies to the group number, all group members will get the message.

What's more, whenever a new member is added to a group, he or she must respond by the first few messages in order to stay in. That's why we set the limit at 50 people per group. We've found that larger groups tend to get very noisy and unwieldy.